3An inequality compares two quantities and typically uses one of these symbols: <is less thanis greater thanis less than or equal tois greater than or equal to
4Additional Example 1: Completing an Inequality Compare. Write < or >.A. 23 –>B. 5(12)<
5Try This: Example 1Compare. Write < or >.A. 19 –<B. 4(15)>
6An inequality that contains a variable is an algebraic inequality. A number that makes an inequality true is a solution of the inequality.The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.
7Word Phrase Sample Solutions InequalitySample SolutionsSolution Setx is less than 5x < 5x = 44 < 5x = 2.12.1 < 5
8Word Phrase Sample Solutions InequalitySample SolutionsSolution Sety is less than or equal to 2y is at most 2y 2y = 00 2y = 1.51.5 2–3 –2 –
9Solving inequalities is the same as solving an equation, but with 1 exception – when you multiply or divide by a negative #.
10Joke of the dayA new teacher was trying to make use of her psychology courses.She started her class by saying, "Everyone who thinks you're stupid, stand up!“ After a few seconds, Little Johnny stood up. The teacher said, "Do you think you're stupid, Little Johnny?" "No, ma'am, but I hate to see you standing there all by yourself!"
11Solve and graph the inequality. A. x 8–2.5–2.5Subtract 2.5 from both sides.x 5.5
12Solve and graph the inequality. B. 5t > 155t > 15Divide both sides by 5.55t > 3
13Solve and graph the inequality. C. w – 1 < 8Add 1 to both sides.w < 9–
14Solve and graph the inequality. 4D. 3 3 p44 •4 •Multiply both sides by 4.12 p
15Lesson Quiz Use < or > to compare each inequality. (2) –Solve and graph each inequality.3. k + 9 < 124. 3 5. A school bus can hold 64 passengers. Three classes would like to use the bus for a field trip. Each class has 21 students. Write and solve an inequality to determine whether all three classes will fit on the bus.>>k< 3–5 –4–3–2–m26 m–4 –3–2–3(21) 64; 63 64; yes?
17Write an equation & solve Homework outWarm-upWrite an equation & solveThe average weight of an elephant is 5,450 kg. This is 4,270 kg more than the average weight of a giraffe. What is the average weight of the giraffe?